So I don’t know if my understanding matches what’s generally understood by “classic”, but in my mind there are two “levels” to this: The first level would be texts written in kobun, i.e. classical literary Japanese that’s pretty different from modern Japanese so I wouldn’t stand the slightest chance in understanding it. The second level would be texts written before the major script reform in 1945/46.
For your list of authors:
太宰 and 芥川 are of course super-well known authors.
小泉 八雲 (whose name at the time of birth was Lafcadio Hearn) lived in Japan for 15 years (until he died) and allowed the West go gain a deep glance into the old Japan.
Also, look what I have on my shelf!
My neighbor gave this to me because “you do Japanese, right?”
(the subtitle says “Life and experiences/adventures in old Japan”)
伊藤 左千夫 is unknown to me. But he seems to be a poet rather than a writer, so there’s that. (Not going to touch poets any time soon, if ever )
森鴎外 is also a very well-known author, although he was a medical doctor by profession. He spent some time in Germany and was a bit of the inverse of Hearn in that he opened the Western world to his Japanese readership. I just listened to a talk about him where it was mentioned that he wrote like crazy, and until today not all of his writings have been covered academically yet
I know him because I read 高瀬舟 with a reading circle at some point (and liked it a lot; I found it to be quite thought-provoking). That one was not too difficult actually.
Regarding whether a certain text is a classic or not: I think many of these authors produced many many texts (short stories are still popular in Japan nowadays, but I feel like back in the day there were hardly any authors who would write really long books - Soseki might be an exception there). So I wouldn’t worry too much whether a given text is actually a classic or not. The authors definitely are.
Bookwalker features some editions and they are around 250 pages, so… it was probably shortened slightly